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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 348082.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348082.k1 | 348082k2 | \([1, 0, 1, -16675, 4076062]\) | \(-3463512697/46512704\) | \(-6885549486433856\) | \([]\) | \(1824768\) | \(1.7206\) | |
348082.k2 | 348082k1 | \([1, 0, 1, 1840, -145358]\) | \(4657463/64484\) | \(-9545946266276\) | \([]\) | \(608256\) | \(1.1713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348082.k have rank \(2\).
Complex multiplication
The elliptic curves in class 348082.k do not have complex multiplication.Modular form 348082.2.a.k
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.